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3 questions with no upvoted or accepted answers
5
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Are the symmetric groups integrable as Hopf algebras?
Let $G$ be a group. For $g,h \in G$, let $[g,h]=g^{-1}h^{-1}gh$ be a commutator. The normal subgroup $G' = \langle [g,h] \ | \ g,h \in G \rangle$ is called the commutator subgroup or derived subgroup. ...
4
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Is the associated grouplike $\gamma=uS(u)^{-1}$ of a quasi-triangular Hopf algebra always the square of another grouplike?
Let $(H,R)$ be a finite-dimensional quasi-triangular Hopf algebra, lets say generated by group-like and skew-primitive elements (I actually need it for $H$ fin. dim. pointed with $G(H)$ abelian). Let $...
3
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What happens geometrically when you take associated-graded (or complete, ...) of a group ring at its augmentation ideal?
I am interested in the following functor from Monoids (in $\text{Set}$) to Graded Lie Algebras (over a fixed field of characteristic $0$). (By "graded" I mean only that my Lie algebras have some ...